Modal Specifications for Probabilistic Timed Systems

TL;DR

This paper introduces a new modal specification language for probabilistic timed systems, enabling formal reasoning about complex embedded and mobile systems with probabilistic and timing aspects.

Contribution

It generalizes existing formalisms by defining abstract probabilistic timed automata with refinement notions and compositional operations, enhancing specification and analysis capabilities.

Findings

Defined a modal specification language for probabilistic timed systems.

Introduced refinement notions and discussed consistency including time-divergence.

Established compositionality results for a subclass of models.

Abstract

Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal automata were introduced for specifying and reasoning about component-based designs for embedded and mobile systems. These respectively generalize modal specification theories for timed and probabilistic systems. In this paper, we define a modal specification language for combined probabilistic timed systems, called abstract probabilistic timed automata, which generalizes existing formalisms. We introduce appropriate syntactic and semantic refinement notions and discuss consistency of our specification language, also with respect to time-divergence. We identify a subclass of our models for which we define the fundamental operations for abstraction, conjunction and parallel composition, and show several compositionality results.